The rising adoption of machine learning in high energy physics and lattice field theory necessitates the re-evaluation of common methods that are widely used in computer vision, which, when applied to problems in physics, can lead to significant drawbacks in terms of performance and generalizability. One particular example for this is the use of neural network architectures that do not reflect the underlying symmetries of the given physical problem. In this work, we focus on complex scalar field theory on a two-dimensional lattice and investigate the benefits of using group equivariant convolutional neural network architectures based on the translation group. For a meaningful comparison, we conduct a systematic search for equivariant and non-equivariant neural network architectures and apply them to various regression and classification tasks. We demonstrate that in most of these tasks our best equivariant architectures can perform and generalize significantly better than their non-equivariant counterparts, which applies not only to physical parameters beyond those represented in the training set, but also to different lattice sizes.

翻译：在高能物理学和拉蒂球场理论中,机器学习的采用程度不断提高,因此有必要重新评估计算机视觉中广泛使用的通用方法,这些方法在应用到物理问题时,可能会在性能和可概括性方面造成重大缺陷。这方面的一个特别例子是,使用不反映特定物理问题基本对称的神经网络结构。在这项工作中,我们侧重于关于二维阵列的复杂的伸缩场理论,并调查使用基于翻译组群的集团等同神经网络结构的益处。为了进行有意义的比较,我们系统地搜索等同性和非等异性神经网络结构,并将其应用于各种回归和分类任务。我们证明,在大多数这些任务中,我们最好的等离异性结构能够比非等异性对应机构更好地运行和概括。 后者不仅适用于在培训组中代表的物理参数,而且还适用于不同的悬浮体大小。